Open the interactive version of the normal tables. (Opens a separate browser window.)
Obtain some pictures of normal curves. Print them out and use them to help solve problems.
1. The Graduate Record Examination (GRE) is widely used to help predict the performance of applicants to graduate school. The range of possible scores on a GRE is 200 to 900. The math department at a university finds that the scores of its applicants on the verbal portion of the GRE (VGRE) are approximately normal with mean m = 612 and standard deviation s = 103. If we select an applicant file at random, find
2. The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 264 days and standard deviation 16 days.
3. The rate of return on stock indexes (which combine many individual stocks) is approximately normal. Since the Standard and 1945, Poor's 500 index has had a mean yearly return of about 12%, with a standard deviation of about 16.5%. Assume the normal distribution is the distribution of yearly returns over a long period.
Some of your results might be a little different; I've used a better table (more accuracy). If you're real close -- you're right!
1. a) 0.0340, b) 0.9462, c) z = 1.28, so go 1.28 stdevs below the mean: 612 - 1.28(103) = 480.16.
2. a) 0.1908, b) 0.5794, c) = z = 2.05, so go 2.05 stdevs above the mean: 264 + 2.05(16) = 296.8 days.
3. a) -21% to 45%, -4.5% to 28.5%, b) 0.2335, c) 0.2154, d) use z = .674 and z = -.674, go .674 stdevs above and below the mean to arrive at (0.88%, 23.12%).